%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL109-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:05:40 PM UTC 2026
% Result : Unsatisfiable 30.63s 7.36s
% Output : CNFRefutation 30.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 66 ( 66 unt; 5 def)
% Number of atoms : 120 ( 65 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-4 aty)
% Number of variables : 82 ( 0 sgn 82 !; 0 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X0] : implies(truth,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_1) ).
fof(f5,axiom,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_3) ).
fof(f8,axiom,
! [X0] : implies(X0,X0) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1) ).
fof(f9,plain,
! [X0] : truth = implies(X0,X0),
inference(reorient_equations,[],[f8]) ).
fof(f11,axiom,
! [X0] : implies(X0,truth) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_3) ).
fof(f12,plain,
! [X0] : truth = implies(X0,truth),
inference(reorient_equations,[],[f11]) ).
fof(f13,axiom,
! [X0,X1] : implies(X0,implies(X1,X0)) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_4) ).
fof(f14,plain,
! [X0,X1] : truth = implies(X0,implies(X1,X0)),
inference(reorient_equations,[],[f13]) ).
fof(f15,axiom,
! [X2,X0,X1] : ifeq(implies(X0,X1),implies(X1,X2),implies(X0,X2),truth) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_5) ).
fof(f16,plain,
! [X2,X0,X1] : truth = ifeq(implies(X0,X1),implies(X1,X2),implies(X0,X2),truth),
inference(reorient_equations,[],[f15]) ).
fof(f17,axiom,
! [X2,X0,X1] : implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_6) ).
fof(f18,plain,
! [X2,X0,X1] : truth = implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
! [X2,X0,X1] : implies(X0,implies(X1,X2)) = implies(X1,implies(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_7) ).
fof(f25,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_mv_4) ).
fof(f26,plain,
truth != implies(implies(implies(a,b),implies(b,a)),implies(b,a)),
inference(reorient_equations,[],[f25]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,plain,
! [X0: $i] : implies(truth,X0) = X0,
inference(cnf_transformation,[],[f2]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_70,plain,
! [X0: $i] : implies(X0,X0) = truth,
inference(cnf_transformation,[],[f9]) ).
tcf(c_72,plain,
! [X0: $i] : implies(X0,truth) = truth,
inference(cnf_transformation,[],[f12]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] : implies(X0,implies(X1,X0)) = truth,
inference(cnf_transformation,[],[f14]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(implies(X0,X1),implies(X1,X2),implies(X0,X2),truth) = truth,
inference(cnf_transformation,[],[f16]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))) = truth,
inference(cnf_transformation,[],[f18]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] : implies(X0,implies(X1,X2)) = implies(X1,implies(X0,X2)),
inference(cnf_transformation,[],[f19]) ).
tcf(c_80,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
inference(cnf_transformation,[],[f26]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(X0,X1),implies(X2,implies(implies(X2,X0),X1))) = truth,
inference(demodulation,[status(thm)],[c_75,c_76]) ).
tcf(c_127,plain,
implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth,
inference(demodulation,[status(thm)],[c_80,c_76]) ).
tcf(c_135,definition,
iPr_def_10 = implies(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_136,definition,
iPr_def_11 = implies(iPr_def_10,a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_137,definition,
iPr_def_12 = implies(b,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_138,definition,
iPr_def_13 = implies(iPr_def_12,a),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_139,definition,
iPr_def_14 = implies(b,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_141,plain,
iPr_def_14 != truth,
inference(demodulation,[status(thm)],[c_127,c_135,c_136,c_137,c_138,c_139]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(X0,X1),implies(X2,implies(implies(X2,X0),X1))) = truth,
inference(demodulation,[status(thm)],[c_126]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i,X2: $i] : implies(X0,implies(X1,X2)) = implies(X1,implies(X0,X2)),
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(implies(X0,X1),implies(X1,X2),implies(X0,X2),truth) = truth,
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i] : implies(X0,implies(X1,X0)) = truth,
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_150,plain,
! [X0: $i] : implies(X0,truth) = truth,
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_152,plain,
! [X0: $i] : implies(X0,X0) = truth,
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_155,plain,
! [X0: $i] : implies(truth,X0) = X0,
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_358,plain,
implies(b,iPr_def_10) = truth,
inference(superposition,[status(thm)],[c_135,c_149]) ).
tcf(c_370,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(implies(X0,X1),X2),implies(X1,implies(truth,X2))) = truth,
inference(superposition,[status(thm)],[c_149,c_142]) ).
tcf(c_373,plain,
! [X0: $i,X1: $i,X2: $i] : implies(X0,implies(implies(implies(X1,X0),X2),X2)) = truth,
inference(demodulation,[status(thm)],[c_370,c_155,c_147]) ).
tcf(c_410,plain,
! [X0: $i] : implies(iPr_def_10,implies(X0,a)) = implies(X0,iPr_def_11),
inference(superposition,[status(thm)],[c_136,c_147]) ).
tcf(c_411,plain,
! [X0: $i] : implies(b,implies(X0,iPr_def_11)) = implies(X0,iPr_def_12),
inference(superposition,[status(thm)],[c_137,c_147]) ).
tcf(c_413,plain,
! [X0: $i] : implies(b,implies(X0,iPr_def_13)) = implies(X0,iPr_def_14),
inference(superposition,[status(thm)],[c_139,c_147]) ).
tcf(c_513,plain,
! [X0: $i] : ifeq(implies(X0,b),iPr_def_14,implies(X0,iPr_def_13),truth) = truth,
inference(superposition,[status(thm)],[c_139,c_148]) ).
tcf(c_827,plain,
! [X0: $i] : implies(b,implies(X0,iPr_def_10)) = implies(X0,truth),
inference(superposition,[status(thm)],[c_358,c_147]) ).
tcf(c_833,plain,
! [X0: $i] : implies(b,implies(X0,iPr_def_10)) = truth,
inference(demodulation,[status(thm)],[c_827,c_150]) ).
tcf(c_7472,plain,
implies(iPr_def_10,iPr_def_13) = implies(iPr_def_12,iPr_def_11),
inference(superposition,[status(thm)],[c_138,c_410]) ).
tcf(c_8262,plain,
implies(b,implies(iPr_def_12,iPr_def_11)) = implies(iPr_def_10,iPr_def_14),
inference(superposition,[status(thm)],[c_7472,c_413]) ).
tcf(c_8304,plain,
implies(iPr_def_10,iPr_def_14) = truth,
inference(demodulation,[status(thm)],[c_8262,c_152,c_411]) ).
tcf(c_9141,plain,
implies(implies(iPr_def_14,iPr_def_10),iPr_def_10) = implies(truth,iPr_def_14),
inference(superposition,[status(thm)],[c_8304,c_153]) ).
tcf(c_9151,plain,
implies(implies(iPr_def_14,iPr_def_10),iPr_def_10) = iPr_def_14,
inference(demodulation,[status(thm)],[c_9141,c_155]) ).
tcf(c_9399,plain,
implies(b,iPr_def_14) = truth,
inference(superposition,[status(thm)],[c_9151,c_833]) ).
tcf(c_12080,plain,
implies(implies(iPr_def_14,b),b) = implies(truth,iPr_def_14),
inference(superposition,[status(thm)],[c_9399,c_153]) ).
tcf(c_12093,plain,
implies(implies(iPr_def_14,b),b) = iPr_def_14,
inference(demodulation,[status(thm)],[c_12080,c_155]) ).
tcf(c_23775,plain,
ifeq(iPr_def_14,iPr_def_14,implies(implies(iPr_def_14,b),iPr_def_13),truth) = truth,
inference(superposition,[status(thm)],[c_12093,c_513]) ).
tcf(c_23789,plain,
implies(implies(iPr_def_14,b),iPr_def_13) = truth,
inference(demodulation,[status(thm)],[c_23775,c_156]) ).
tcf(c_35603,plain,
implies(b,implies(truth,iPr_def_13)) = truth,
inference(superposition,[status(thm)],[c_23789,c_373]) ).
tcf(c_35616,plain,
truth = iPr_def_14,
inference(demodulation,[status(thm)],[c_35603,c_155,c_413]) ).
tcf(c_35927,plain,
iPr_def_14 != iPr_def_14,
inference(demodulation,[status(thm)],[c_141,c_35616]) ).
tcf(c_35928,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_35927]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL109-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Wed Sep 23 21:57:33 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 Running UEQ theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 30.63/7.36 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 30.63/7.36 % SZS status Started for theBenchmark.p
% 30.63/7.36 % SZS status Unsatisfiable for theBenchmark.p
% 30.63/7.36
% 30.63/7.36 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 30.63/7.36
% 30.63/7.36 % ------ iProver source info
% 30.63/7.36
% 30.63/7.36 % git: date: 2026-07-19 20:42:38 +0200
% 30.63/7.36 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 30.63/7.36 % git: non_committed_changes: false
% 30.63/7.36
% 30.63/7.36 % ------ Parsing...% successful
% 30.63/7.36
% 30.63/7.36
% 30.63/7.36 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 30.63/7.36
% 30.63/7.36 % ------ Preprocessing... sup_sim: 3 sf_s rm: 0 0s sf_e pe_s pe_e %
% 30.63/7.36
% 30.63/7.36 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 30.63/7.36
% 30.63/7.36 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 30.63/7.36 % ------ Proving...
% 30.63/7.36 % ------ Problem Properties
% 30.63/7.36
% 30.63/7.36 %
% 30.63/7.36 % clauses 22
% 30.63/7.36 % conjectures 0
% 30.63/7.36 % EPR 1
% 30.63/7.36 % Horn 22
% 30.63/7.36 % unary 22
% 30.63/7.36 % binary 0
% 30.63/7.36 % lits 22
% 30.63/7.36 % lits eq 22
% 30.63/7.36 % fd_pure 0
% 30.63/7.36 % fd_pseudo 0
% 30.63/7.36 % fd_cond 0
% 30.63/7.36 % fd_pseudo_cond 0
% 30.63/7.36 % AC symbols 0
% 30.63/7.36
% 30.63/7.36 % ------ Input Options Time Limit: Unbounded
% 30.63/7.36
% 30.63/7.36
% 30.63/7.36 % ------
% 30.63/7.36 % Current options:
% 30.63/7.36 % ------
% 30.63/7.36
% 30.63/7.36
% 30.63/7.36 %
% 30.63/7.36
% 30.63/7.36 % ------ Proving...
% 30.63/7.36 %
% 30.63/7.36
% 30.63/7.36 % SZS status Unsatisfiable for theBenchmark.p
% 30.63/7.36
% 30.63/7.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 30.63/7.36
% 30.63/7.36
%------------------------------------------------------------------------------